Robust policy evaluation for non-rectangular uncertainty set is generally NP-hard, even in approximation. Consequently, existing approaches suffer from either exponential iteration complexity or significant accuracy gaps. Interestingly, we identify a powerful class of Lp-bounded uncertainty sets that avoid these complexity barriers due to their structural simplicity. We further show that this class can be decomposed into infinitely many sa-rectangular Lp-bounded sets and leverage its structural properties to derive a novel dual formulation for Lp robust Markov Decision Processes (MDPs). This formulation reveals key insights into the adversary's strategy and leads to the first polynomial-time robust policy evaluation algorithm for L1-normed non-rectangular robust MDPs.

Markov decision processes (MDPs) often suffer from the sensitivity issue under model ambiguity. In recent years, robust MDPs have emerged as an effective framework to overcome this challenge. Distributionally robust MDPs extend the robust MDP framework by incorporating distributional information of the uncertain model parameters to alleviate the conservative nature of robust MDPs.

Typically, deep RL algorithms learn a policy in an online trial-and-error fashion using millions to billions of data.

We provide a closed-form expression for the worst occupation measure.

However, they do not account for transition uncertainty, whereas learning robust policies can be computationally expensive.

Neural Information Processing Systems http://nips.cc/

Robust MDPs (RMDPs) can be used to compute policies with provable worst-case guarantees in reinforcement learning. The quality and robustness of an RMDP solution are determined by the ambiguity set---the set of plausible transition probabilities---which is usually constructed as a multi-dimensional confidence region. Existing methods construct ambiguity sets as confidence regions using concentration inequalities which leads to overly conservative solutions. This paper proposes a new paradigm that can achieve better solutions with the same robustness guarantees without using confidence regions as ambiguity sets. To incorporate prior knowledge, our algorithms optimize the size and position of ambiguity sets using Bayesian inference. Our theoretical analysis shows the safety of the proposed method, and the empirical results demonstrate its practical promise.

In recent years, robust Markov decision processes (MDPs) have emerged as a prominent modeling framework for dynamic decision problems affected by uncertainty. In contrast to classical MDPs, which only account for stochasticity by modeling the dynamics through a stochastic process with a known transition kernel, robust MDPs additionally account for ambiguity by optimizing in view of the most adverse transition kernel from a prescribed ambiguity set. In this paper, we develop a novel solution framework for robust MDPs with $s$-rectangular ambiguity sets that decomposes the problem into a sequence of robust Bellman updates and simplex projections. Exploiting the rich structure present in the simplex projections corresponding to $\phi$-divergence ambiguity sets, we show that the associated $s$-rectangular robust MDPs can be solved substantially faster than with state-of-the-art commercial solvers as well as a recent first-order solution scheme, thus rendering them attractive alternatives to classical MDPs in practical applications.

Robust Markov decision processes (MDPs) aim to handle changing or partially known system dynamics. To solve them, one typically resorts to robust optimization methods. However, this significantly increases computational complexity and limits scalability in both learning and planning.